There are no SkyTeam options that will get you around inside Australia and New Zealand. DJ is your best bet. If you've got DL status (GM, PM, or DM), you'll get lounge access at least. Probably what I'd do, however, is look at KE to AKL, then DJ (or whoever is cheapest) for AKL-MEL as a one-way. Open-jaw your way back to RDU with KE. Just check the fare class that you're getting from KE to make sure you'll get miles from DL. (Unfortunately, MEL-ICN and ICN-AKL are not daily flights, so this only works if KE's running those flights on the days you need.) If you're only looking for RDM and not MQM, you might see about Virgin Australia selling you the ticket with stopovers. Lots of folks on the DL forum have flown VA from LAX and given positive reports.